Uniqueness and global stability of the instanton in non local evolution equations. (English) Zbl 0821.45003
The authors consider the equation (1) \({\partial m \over \partial t} = - m + \text{tanh} \{\beta J^* m\}\), where \(m : \mathbb{R} \times \mathbb{R}_ + \to \mathbb{R}\); \(\mathbb{R} \ni \beta > 1\); \(J \in C^ 2 [-1,1]\) is a nonnegative, even function with the integral equal to 1; \((J^*m) (x) : = \int J (x - y) m(y)dy\). Results on existence, uniqueness and global stability of special stationary solutions of (1) called instantons are proved.
Reviewer: V.Kravchenko (Mexico)
MSC:
45K05 | Integro-partial differential equations |
45M10 | Stability theory for integral equations |
45G10 | Other nonlinear integral equations |
82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |